Temperature dependence of the hydrated electron's excited-state relaxation. I. Simulation predictions of resonance Raman and pump-probe transient absorption spectra of cavity and non-cavity models.

We use one-electron non-adiabatic mixed quantum/classical simulations to explore the temperature dependence of both the ground-state structure and the excited-state relaxation dynamics of the hydrated electron. We compare the results for both the traditional cavity picture and a more recent non-cavity model of the hydrated electron and make definite predictions for distinguishing between the different possible structural models in future experiments. We find that the traditional cavity model shows no temperature-dependent change in structure at constant density, leading to a predicted resonance Raman spectrum that is essentially temperature-independent. In contrast, the non-cavity model predicts a blue-shift in the hydrated electron's resonance Raman O-H stretch with increasing temperature. The lack of a temperature-dependent ground-state structural change of the cavity model also leads to a prediction of little change with temperature of both the excited-state lifetime and hot ground-state cooling time of the hydrated electron following photoexcitation. This is in sharp contrast to the predictions of the non-cavity model, where both the excited-state lifetime and hot ground-state cooling time are expected to decrease significantly with increasing temperature. These simulation-based predictions should be directly testable by the results of future time-resolved photoelectron spectroscopy experiments. Finally, the temperature-dependent differences in predicted excited-state lifetime and hot ground-state cooling time of the two models also lead to different predicted pump-probe transient absorption spectroscopy of the hydrated electron as a function of temperature. We perform such experiments and describe them in Paper II [E. P. Farr et al., J. Chem. Phys. 147, 074504 (2017)], and find changes in the excited-state lifetime and hot ground-state cooling time with temperature that match well with the predictions of the non-cavity model. In particular, the experiments reveal stimulated emission from the excited state with an amplitude and lifetime that decreases with increasing temperature, a result in contrast to the lack of stimulated emission predicted by the cavity model but in good agreement with the non-cavity model. Overall, until ab initio calculations describing the non-adiabatic excited-state dynamics of an excess electron with hundreds of water molecules at a variety of temperatures become computationally feasible, the simulations presented here provide a definitive route for connecting the predictions of cavity and non-cavity models of the hydrated electron with future experiments.

Temperature dependence of the hydrated electron's excited-state relaxation. II. Elucidating the relaxation mechanism through ultrafast transient absorption and stimulated emission spectroscopy.

The structure of the hydrated electron, particularly whether it exists primarily within a cavity or encompasses interior water molecules, has been the subject of much recent debate. In Paper I [C.-C. Zho et al., J. Chem. Phys. 147, 074503 (2017)], we found that mixed quantum/classical simulations with cavity and non-cavity pseudopotentials gave different predictions for the temperature dependence of the rate of the photoexcited hydrated electron's relaxation back to the ground state. In this paper, we measure the ultrafast transient absorption spectroscopy of the photoexcited hydrated electron as a function of temperature to confront the predictions of our simulations. The ultrafast spectroscopy clearly shows faster relaxation dynamics at higher temperatures. In particular, the transient absorption data show a clear excess bleach beyond that of the equilibrium hydrated electron's ground-state absorption that can only be explained by stimulated emission. This stimulated emission component, which is consistent with the experimentally known fluorescence spectrum of the hydrated electron, decreases in both amplitude and lifetime as the temperature is increased. We use a kinetic model to globally fit the temperature-dependent transient absorption data at multiple temperatures ranging from 0 to 45 °C. We find the room-temperature lifetime of the excited-state hydrated electron to be 137±40 fs, in close agreement with recent time-resolved photoelectron spectroscopy (TRPES) experiments and in strong support of the "non-adiabatic" picture of the hydrated electron's excited-state relaxation. Moreover, we find that the excited-state lifetime is strongly temperature dependent, changing by slightly more than a factor of two over the 45 °C temperature range explored. This temperature dependence of the lifetime, along with a faster rate of ground-state cooling with increasing bulk temperature, should be directly observable by future TRPES experiments. Our data also suggest that the red side of the hydrated electron's fluorescence spectrum should significantly decrease with increasing temperature. Overall, our results are not consistent with the nearly complete lack of temperature dependence predicted by traditional cavity models of the hydrated electron but instead agree qualitatively and nearly quantitatively with the temperature-dependent structural changes predicted by the non-cavity hydrated electron model.

Thermal Equilibration Controls H-Bonding and the Vertical Detachment Energy of Water Cluster Anions.

One of the outstanding puzzles in the photoelectron spectroscopy of water anion clusters, which serve as precursors to the hydrated electron, is that the excess electron has multiple vertical detachment energies (VDEs), with different groups seeing different distributions of VDEs. We have studied the photoelectron spectroscopy of water cluster anions using simulation techniques designed to mimic the different ways that water cluster anions are produced experimentally. Our simulations take advantage of density functional theory-based Born-Oppenheimer molecular dynamics with an optimally tuned range-separated hybrid functional that is shown to give outstanding accuracy for calculating electron binding energies for this system. We find that our simulations are able to accurately reproduce the experimentally observed VDEs for cluster anions of different sizes, with different VDE distributions observed depending on how the water cluster anions are prepared. For cluster anion sizes up to 20 water molecules, we see that the excess electron always resides on the surface of the cluster and that the different discrete VDEs result from the discrete number of hydrogen bonds made to the electron by water molecules on the surface. Clusters that are less thermally equilibrated have surface waters that tend to make single H-bonds to the electron, resulting in lower VDEs, while clusters that are more thermally equilibrated have surface waters that prefer to make two H-bonds to the electron, resulting in higher VDEs.

Time-Resolved Photoelectron Spectroscopy of the Hydrated Electron: Comparing Cavity and Noncavity Models to Experiment.

We use nonadiabatic mixed quantum/classical molecular dynamics to simulate recent time-resolved photoelectron spectroscopy (TRPES) experiments on the hydrated electron, and compare the results for both a cavity and a noncavity simulation model to experiment. We find that cavity-model hydrated electrons show an "adiabatic" relaxation mechanism, with ground-state cooling that is fast on the time scale of the internal conversion, a feature that is in contrast to the TRPES experiments. A noncavity hydrated electron model, however, displays a "nonadiabatic" relaxation mechanism, with rapid internal conversion followed by slower ground-state cooling, in good qualitative agreement with experiment. We also show that the experimentally observed early time red shift and loss of anisotropy of the excited-state TRPES peak are consistent with hydrated electron models with homogeneously broadened absorption spectra, but not with those with inhomogeneously broadened absorption spectra. Finally, we find that a decreasing photoionization cross section upon cooling causes the excited-state TRPES peak to decay faster than the underlying radiationless relaxation process, so that the experimentally observed 60-75 fs peak decay corresponds to an actual excited-state lifetime of the hydrated electron that is more likely ∼100 fs.